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6.17 Consider the linear code
A :=<{(1, 1), (α, 1 + α)}>
over F4, where α is a root of 1 + x + x 2 ∈ F2[x]. Let B be the binary
code {0000, 1100, 1010, 0110} and consider the F2-linear transformation
between F4 and B defined by
φ : 0 → 0000, 1 → 1100, α → 1010, 1 + α → 0110.
Determine all the codewords of the code
C := φ∗(A) = {(φ(c1), φ(c2)) : (c1, c2) ∈ A}.
